Collusion in Atomic Splittable Routing Games

  • Chien-Chung Huang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)


We investigate how collusion affects the social cost in atomic splittable routing games. Suppose that players form coalitions and each coalition behaves as if it were a single player controlling all the flows of its participants. It may be tempting to conjecture that the social cost would be lower after collusion, since there would be more coordination among the players. We construct examples to show that this conjecture is not true. These examples motivates the question:  under what conditions would the social cost of the post-collusion equilibrium be bounded by the social cost of the pre-collusion equilibrium?

We show that if (i) the network is “well-designed” (satisfying a natural condition), and (ii) the delay functions are affine, then collusion is always beneficial for the social cost in the Nash equilibria. On the other hand, if either of the above conditions is unsatisfied, collusion can worsen the social cost. Our main technique is a novel flow-augmenting algorithm to build Nash equilibria.


Nash Equilibrium Social Cost Full Version Delay Function Congestion Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Altman, E., Basar, T., Jimenez, T., Shimkin, N.: Competitive routing in networks with polynomial costs. IEEE Transactions on Automatic Control 47(1), 92–96 (2002)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. In: SODA, pp. 189–198 (2007)Google Scholar
  3. 3.
    Aumann, R.: Acceptable points in geneeral cooperative n-person games. Contributions to the Theory of Games 4 (1959)Google Scholar
  4. 4.
    Bhaskar, U., Fleischer, L., Huang, C.-C.: The price of collusion in series-parallel networks. In: Eisenbrand, F., Shepherd, F.B. (eds.) IPCO 2010. LNCS, vol. 6080, pp. 313–326. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Cominetti, R., Correa, J., Stier-Moses, N.E.: The impact of oligopolistic competition in networks. Operations Research 57(6), 1421–1437 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Atomic congestion games among coalitions. ACM Transactions on Algorithms 4(4) (2008)Google Scholar
  7. 7.
    Harks, T.: Stackelberg strategies and collusion in network games with splittable flow. In: Bampis, E., Skutella, M. (eds.) WAOA 2008. LNCS, vol. 5426, pp. 133–146. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Hayrapetyan, A., Tardos, E., Wexler, T.: The effect of collusion in congestion games. In: STOC, pp. 89–98 (2006)Google Scholar
  9. 9.
    Huang, C.-C.: The price of collusion in series-parallel networks, Technical Report 238, Humboldt-Universität zu Berlin, Institut für Informatik (2011)Google Scholar
  10. 10.
    Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  11. 11.
    Orda, A., Rom, R., Shimkin, N.: Competitive routing in multiuser communication networks. IEEE/ACM Transactions on Networking 1(5), 510–521 (1993)CrossRefGoogle Scholar
  12. 12.
    Roughgarden, T.: Selfish routing with atomic players. In: SODA, pp. 1184–1185 (2005)Google Scholar
  13. 13.
    Roughgarden, T., Schoppmann, F.: Local smoothness and the price of anarchy in atomic splittable congestion game. In: SODA, pp. 255–267 (2011)Google Scholar
  14. 14.
    Roughgarden, T., Tardos, E.: How bad is selfish routing? Journal of the ACM 49(2), 236–259 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Wardrop, J.G.: Some theoretical aspects of road traffic research. In: Proc. Institute of Civil Engineers, Pt. II, vol. 1, pp. 325–378 (1952)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Chien-Chung Huang
    • 1
  1. 1.Humboldt-Universität zu BerlinBerlinGermany

Personalised recommendations